On the Euler function of the Catalan numbers

Luca, Florian; Stănică, Pantelimon

doi:10.1016/j.jnt.2012.02.002

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Cited by 3 publications

(2 citation statements)

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“…Further, Luca in [5] considered ϕ(F n ), where F n is the nth Fibonacci number. In [7], Luca and Stȃnicȃ investigated quotients of the form ϕ(C m )/ϕ(C n ), where C n is the nth Catalan number.…”

Section: Introductionmentioning

confidence: 99%

On Quotients of Values of Euler's Function on Factorials

Nath,

Jha

2021

Preprint

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Recently, there has been some interest in values of arithmetical functions on members of special sequences, such as Euler's totient function ϕ on factorials, linear recurrences, etc. In this article, we investigate, for given positive integers a and b, the least positive integer c = c(a, b) such that the quotient ϕ(c!)/ϕ(a!)ϕ(b!) is an integer. We derive results on the limit of the ratio c(a, b)/(a + b) as a and b tend to infinity. Furthermore, we show that c(a, b) > a + b for all pairs of positive integers (a, b) with an exception of a set of density zero.

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Section: Introductionmentioning

confidence: 99%

On Quotients of Values of Euler's Function on Factorials

Nath,

Jha

2021

Preprint

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“…Further, Luca [5] considered where is the n th Fibonacci number. In [7], Luca and Stănică investigated quotients of the form where is the n th Catalan number.…”

Section: Introductionmentioning

confidence: 99%

On Quotients of Values of Euler’s Function on Factorials

Nath¹,

Jha²

2021

Bull. Aust. Math. Soc.

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We investigate, for given positive integers a and b, the least positive integer $c=c(a,b)$ such that the quotient $\varphi (c!\kern-1.2pt)/\varphi (a!\kern-1.2pt)\varphi (b!\kern-1.2pt)$ is an integer. We derive results on the limit of $c(a,b)/(a+b)$ as a and b tend to infinity and show that $c(a,b)>a+b$ for all pairs of positive integers $(a,b)$ , with the exception of a set of density zero.

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On quotients of values of Euler's function on the Catalan numbers

Bašić

2016

Journal of Number Theory

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On the Euler function of the Catalan numbers

Cited by 3 publications

References 17 publications

On Quotients of Values of Euler's Function on Factorials

On Quotients of Values of Euler's Function on Factorials

On Quotients of Values of Euler’s Function on Factorials

On quotients of values of Euler's function on the Catalan numbers

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